针对线性模型的对抗训练，提出高效优化算法，加速大规模问题求解。
Efficient Optimization Algorithms for Linear Adversarial Training
- 基于变量重构，设计迭代岭回归与投影梯度下降两类专用求解器。
- 在回归与分类任务中均实现更快收敛，显著提升大规模问题求解效率。
- 适合需要快速训练鲁棒线性模型的研究者或工业场景应用。
对抗训练可用于学习对扰动具有鲁棒性的模型。对于线性模型，该问题可表述为凸优化问题。相比深度学习背景下的方法，利用其优化结构可实现更快的收敛速度。然而，通用凸优化求解器在大规模问题上仍效率不足。本文针对线性模型的对抗训练，提出定制化优化算法，使大规模回归与分类问题更具可计算性。针对回归问题，提出基于迭代岭回归的一类求解器；针对分类问题，提出基于投影梯度下降的一类求解器。这些方法基于原问题的扩展变量重构形式。通过数值实验验证了其高效性。
原文摘要 · Abstract (English)
Adversarial training can be used to learn models that are robust against perturbations. For linear models, it can be formulated as a convex optimization problem. Compared to methods proposed in the context of deep learning, leveraging the optimization structure allows significantly faster convergence rates. Still, the use of generic convex solvers can be inefficient for large-scale problems. Here, we propose tailored optimization algorithms for the adversarial training of linear models, which render large-scale regression and classification problems more tractable. For regression problems, we propose a family of solvers based on iterative ridge regression and, for classification, a family of solvers based on projected gradient descent. The methods are based on extended variable reformulations of the original problem. We illustrate their efficiency in numerical examples.
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